

A260002


Sudan Numbers: a(n)= f(n,n,n) where f is the Sudan function.


5




OFFSET

0,2


COMMENTS

The Sudan function is the first discovered not primitive recursive function that is still totally recursive like the wellknown threeargument (or twoargument) Ackermann function ack(a,b,c) (or ack(a,b)).
The Sudan function is defined as follows:
f(0,x,y) = x+y;
f(z,x,0) = x;
f(z,x,y) = f(z1, f(z,x,y1), f(z,x,y1)+y).
Just as the threeargument (or twoargument) Ackermann numbers A189896 (or A046859) are defined to be the numbers that are the answer of ack(n,n,n) (or ack(n,n)) for some natural number n, the Sudan numbers are: a(n) = f(n,n,n).
a(3)> 2^(76*2^(76*2^(76*2^(76*2^76)))) so is too big to be included.


LINKS



EXAMPLE

a(1) = f(1,1,1) = f(0, f(1,1,0), f(1,1,0)+1) = f(0, 1, 2) = 1+2 = 3.


MATHEMATICA

f[z_, x_, y_] := f[z, x, y] =
Piecewise[{{x + y, z == 0}, {x,
z > 0 && y == 0}, {f[z  1, f[z, x, y  1], f[z, x, y  1] + y],
z > 0 && y > 0} }];
a[n_] := f[n, n, n]


PROG

(PARI) f(z, x, y)=if(z, if(y, my(t=f(z, x, y1)); f(z1, t, t+y), x), x+y)


CROSSREFS



KEYWORD

nonn,bref


AUTHOR



STATUS

approved



